A billiard ball moving with a speed of +4 m/s runs head on into the back of another ball moving with a speed of +2 m/s. After the collision the first ball was measured to be moving with a speed of +2 m/s. Find the speed of the second ball.
formula = mivi+m2v2= mivi+m2v2
so far I have something like this: m(+4m/s)m2(+2m/s) = m2(+2m/s)+v2. I believe it is wrong.
The balls exchange speeds in an elastic head-on collision. Thus the second ball leaves at 4 m/s.
Note that total momentum and kinetic energy are conserved as a result. No other final velocity conserves both. The result than Ball #1 leaves at 2 m/s could have been predicted by solving both equations.
To solve this problem, we can use the principle of conservation of momentum. This principle states that in a collision between two objects, the total momentum before the collision is equal to the total momentum after the collision, provided there are no external forces acting on the system.
Let's assign variables to the given information:
Let m1 be the mass of the first ball,
Let m2 be the mass of the second ball,
Let v1i be the initial velocity of the first ball,
Let v2i be the initial velocity of the second ball,
Let v1f be the final velocity of the first ball,
And let v2f be the final velocity of the second ball.
Using the conservation of momentum principle, we can write the equation:
(m1 * v1i) + (m2 * v2i) = (m1 * v1f) + (m2 * v2f)
Given data:
m1 = mass of the first ball
v1i = 4 m/s (initial velocity of the first ball)
m2 = mass of the second ball
v2i = 2 m/s (initial velocity of the second ball)
v1f = 2 m/s (final velocity of the first ball)
Plug the values into the equation:
(m1 * 4) + (m2 * 2) = (m1 * 2) + (m2 * v2f)
Simplifying the equation:
4m1 + 2m2 = 2m1 + m2
To find the speed of the second ball, we need to eliminate m1 from the equation. To do this, we can use the fact that the final velocity of the first ball is equal to the initial velocity of the second ball (v1f = v2i).
Substituting v1f = v2i into the equation, we get:
4m1 + 2m2 = 2m1 + m2
4m1 - 2m1 = m2 - 2m2
2m1 = -m2
2m1/m2 = -1
Now, we don't have enough information to determine the exact values of m1 and m2. However, we can find the ratio between m1 and m2. The ratio is -1/2, which means that the mass of the first ball is half of the mass of the second ball.